# Offset Slider Crank Question

1. Feb 24, 2015

### hopkid

1. The problem statement, all variables and given/known data
a) For the mechanism shown in figure 1 determine for the angle (45°):
i) the velocity (VBO) of the piston relative to the fixed point (O).
ii) the angular velocity of AB about point A.
iii) the acceleration of point B relative to A.
*Note: Link AB is horizontal when angle = 45°.
b) Determine the value of the angle (measured from vertical) when:
i) the velocity of point b = 0.
ii) the angular velocity of link AB a maximum.
c) what is the maximum angular velocity of link AB?

2. Relevant equations
v=lw (a)r = v^2/l

3. The attempt at a solution
l of AO = 50mm = 0.05m
l of AB = 200mm = 0.2m
w of AO = 300 x 2pi/60 = 31.42 rads^-1

ai) V of AO = l of AO x w of AO.
V of A0 = 0.05 x 31.42
V of AO = 1.57ms^-1

*Use this value to draw a velocity diagram (attached).

To confirm using trig,

Sin(45°) = V of BO/1.57
V of BO = 1.57 x Sin(45°)
V of BO = 1.11ms^-1

aii) v=lw therefore w=v/l

w of AB = v of AB/l of AB
w of AB = 1.11/0.2
w of AB = 5.55 rads^-1

aiii) (a of BA)r = v of BA^2/l of BA
(a of BA)r = 1.11^2/0.2
(a of BA)r = 6.16ms^-2

*Tangential velocity is calculated in the acceleration diagram (attached).

Radial acceleration of AO calculated below to use in the diagram.
(a of AO)r = v of AO^2/l of AO
(a of AO)r = 1.57^2/0.05
(a of AO)r = 49.3ms^-2

So, as per the diagram, (a of BA)t = 34.5ms^-2.

This is the part where I am starting to struggle, I have had conformation back from my tutor that the first 3 parts to the question look good but I am struggling with parts b & c.

If someone could help push me in the right direction then it would be very much appreciated. I am after guidance, not answers, I want to learn.

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2. Mar 1, 2015

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Mar 3, 2015

### hopkid

No I have no new information, I've tried to be as thorough as possible with my post because in the past people have asked for more information. I'm really struggling with understanding this, and I'm not too sure why I am not getting any responses?!

4. May 31, 2015

### Mike Greeno

Hi,

Did you have any luck finding out about Q1b and Q1c? I am inclined to think that velocity B=0 occurs when the crank arm and link create a straight line. And max acceleration occurs when they are at right angles. Then its just a case of drawing out the triangle to find theta? Is that anywhere along the right line?

-Mikey